The coordinate plane below represents a town. points a through f are farms in the town.

part a: using the graph above, create a system of inequalities that only contains points d and e in the overlapping shaded regions. explain how the lines will be graphed and shaded on the coordinate grid above. (5 points)

part b: explain how to verify that the points d and e are solutions to the system of inequalities created in part a. (3 points)

part c: chickens can only be raised in the area defined by y > 3x − 4. explain how you can identify farms in which chickens can be raised. (2 points)

The first inequality: y≤-x+6. the graph is a solid line that goes through (0,6) and (6,0) with the shaded area under the line. All the points are in the shaded area. 
the second inequality: y>x+4, the graph is a dotted line going through (0,4) and (-4,0) with the shaded area above the line. Only D and E are in the shaded area.
so only D and E satisfy both inequality. 

To verify if D and E are solutions, plug the coordinates of D (-4,2) and E (-1,5) in the inequality to see if they will make both inequalities true. 
is 2 smaller or equal to -(-4)+6? yes, 2 is smaller than 10
is 2 larger than (-4)+4? yes, 2 is larger than 0.
Do the same with coordinates of E. 

Part C: graph the inequality. the dotted line goes through (0,-4), (1,-1), and the shaded part is above (to the left of) the line. You'll see that A, D, E, F are in the shaded area, suitable for raising chicken.